The issue, a top second-term priority for President Obama, has languished in the House after the Senate passed a bipartisan comprehensive overhaul in June. House GOP leaders are unlikely to consider measures in the two remaining legislative weeks of 2013, and reform advocates say there is a rapidly closing window to address the issue before the 2014 midterm campaigns heat up.

Boehner has spoken frankly of the difficulty in moving the contentious proposals through the Republican House, but he made a point of mentioning immigration at the outset of the press conference on Thursday.

He said he was “encouraged” by Obama’s comments on Tuesday that he would be open to several individual immigration bills as opposed to one comprehensive measure, as long as those pieces addressed all aspects of reform.

“The American people are skeptical of big, comprehensive bills, and they should be,” Boehner said. “The only way to make sure immigration reform works this time is to address these complicated issues one step at a time.”

The Speaker noted that House committees continue to work on legislation and that private conversations are ongoing over how best to handle immigration reform.

Yet as before, he laid out no specific timetable for House votes, and he did not weigh in on the thorniest piece of the immigration puzzle — the question of legal status or citizenship for the estimated 11 million immigrants living in the United States illegally.